Forecasting Intervals

Forecasting Intervals - Forecasting with interval and...

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Forecasting with interval and histogram data Some f nancial applications Javier Arroyo Universidad Complutense de Madrid Department of Computer Science and Arti f cial Intelligence 28040 Madrid, Spain Gloria González-Rivera University of California, Riverside Deaprtment of Economics Riverside, CA 92521 Carlos Maté Universidad Ponti f cia de Comillas Institute for Research in Technology (IIT) Advanced Technical Faculty of Engineering (ICAI) 28015 Madrid, Spain We thank the referees and the editors for useful and constructive comments. González-Rivera acknowledges the f nancial support provided by the University Scholar Award. Ma ´ te acknowledges the f nancial support provided by the project "Forecasting models from symbolic data (PRESIM)" from Universidad Ponti f cia Comillas. Corresponding author: gloria.gonzalez@ucr.edu, tel (951) 827-1590, fax (951) 827-5685. 1
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ABSTRACT Data sets across many disciplines are becoming consistently large and they bring with them the need of new methods for processing information. We introduce the analysis of interval-valued and histogram-valued data sets as an alternative to classic single-valued data sets and we show the promise of this approach on dealing with economic and f nancial data. Being our current focus the prediction problem, we explore two di f erent venues to produce a forecast with interval time series (ITS) and histogram time series (HTS). For ITS, we adapt classical regression methods and time series strategies for model building and prediction. For ITS and HTS, we implement f ltering techniques, such as smoothing, and non-parametric methods such as the k-NN. We need interval arithmetic in ITS and the concept of a barycentric histogram in HTS to compute the appropriate averages required by smoothing and k-NN. The assessment of the forecast error also requires the introduction of dissimilarity measures like a kernel based distance for ITS and the Wasserstein and Mallows distances for HTS. We apply the proposed methods to predict the daily interval low/high prices of the SP500 index and the weekly cross-sectional histogram of the returns to the constituents of the SP500 index. Overall, k-NN methods perform very well. Key Words : Interval-valued data, histogram-valued data, interval arithmetic, dissimilarity measures, exponential smoothing, k-NN, Wasserstein distance, Mallows distance. JEL Classi f cation: C22, C53 2
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Article Outline 1. Introduction 2. Interval data 2.1 Preliminaries 2.2 The regression problem 2.3 The prediction problem 2.3.1 Accuracy of the forecast 2.3.2 Smoothing methods 2.3.3 k-NN method 2.4 Interval-valued dispersion : low/high SP500 prices 3. Histogram data 3.1 Preliminaries 3.2 The prediction problem 3.2.1 Accuracy of the forecast 3.2.2 The barycentric histogram 3.2.3 Exponential smoothing 3.2.4 k-NN method 3.3 Histogram forecast: SP500 returns 4. Summary and conclusions 5. References 3
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1 Introduction In Economics we customarily deal with classical data sets. When we collect information on a set of variables of interest, either in a cross-sectional or/and time series framework,
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Forecasting Intervals - Forecasting with interval and...

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